Quasiclassical Trajectory Simulations Research Articles

Variable Mechanisms for Cobalt-Catalyzed Alkyne Dimerization Pinpointed by Quasi-Classical Trajectory Simulations

Variable Mechanisms for Cobalt-Catalyzed Alkyne Dimerization Pinpointed by Quasi-Classical Trajectory Simulations

Dynamics of the Cl + CH3CN reaction on an automatically-developed full-dimensional abinitio potential energy surface.

A full-dimensional analytical potential energy surface (PES) is developed for the Cl + CH3CN reaction following our previous work on the benchmark abinitio characterization of the stationary points. The spin-orbit-corrected PES is constructed using the Robosurfer program and a fifth-order permutationally invariant polynomial method for fitting the high-accuracy energy points determined by a ManyHF-based coupled-cluster/triple-zeta-quality composite method. Quasi-classical trajectory simulations are performed at six collision energies between 10 and 60kcal mol-1. Multiple low-probability product channels are found, including isomerization to isonitrile (CH3NC), but out of the eight possible channels, only the H-abstraction has significant reaction probability; thus, detailed dynamics studies are carried out only for this reaction. The cross sections and opacity functions show that the probability of the H-abstraction reaction increases with increasing collision energy (Ecoll). Scattering angle, initial attack angle, and product relative translational energy distributions indicate that the mechanism changes with the collision energy from indirect/rebound to direct stripping. The distribution of initial attack angles shows a clear preference for methyl group attack but with different angles at different Ecoll values. Post-reaction energy distributions show that the energy transfer is biased toward the products' relative translational energy instead of their internal energy. Rotational and vibrational energy have about the same amount of contribution to the internal energy in the case of both products (HCl and CH2CN), i.e., both of them are formed with high rotational excitations. HCl is produced mostly in the ground vibrational state, while a notable fraction of CH2CN is formed with vibrational excitation.

Computational study on the bifurcation mechanism in the H2CO− + CH3Cl →CH3CH2O + Cl−/H2CO + CH3 + Cl− reaction: The importance of intramolecular vibrational redistributions

We have investigated the bifurcation dynamics of the H2CO− + CH3Cl →CH3CH2O + Cl− (C-substitution channel)/H2CO + CH3 + Cl− (electron transfer channel) reaction using three different molecular dynamics (MD) methods: quasi-classical trajectory (QCT), classical MD, and ring-polymer MD simulations. All MD calculations were performed using the on-the-fly approach at the ab initio molecular orbital theory level. We found that the C-substitution channel is dominant in the classical and ring-polymer MD calculations, while the electron transfer channel is dominant in the QCT calculations. The different bifurcation mechanisms in the types of MD simulations were investigated using supervised machine-learning classification. This difference is attributed to the varying efficiency of the intramolecular vibrational redistribution process among the different MD methods. Thus, in the bifurcation mechanism of the H2CO− + CH3Cl reaction, the bifurcation fractions are primarily determined by the vibrational dynamics occurring in the later stages of the reaction.

High-Energy Reaction Dynamics of N3.

The atom-exchange and atomization dissociation dynamics for the N(4S) + N2(1Σg+) reaction are studied using a reproducing kernel Hilbert space (RKHS)-based, global potential energy surface (PES) at the MRCI-F12/aug-cc-pVTZ-F12 level of theory (MRCI, multireference configuration interaction). For the atom exchange reaction (NANB + NC → NANC + NB), computed thermal rates and their temperature dependence from quasi-classical trajectory (QCT) simulations agree to within error bars with the available experiments. Companion QCT simulations using a recently published CASPT2-based PES confirm these findings. For the atomization reaction, leading to three N(4S) atoms, the computed rates from the RKHS-PES overestimate the experimentally reported rates by 1 order of magnitude, whereas those from the permutationally invariant polynomial (PIP)-PES agree favorably, and the T dependence of both computations is consistent with the experiment. These differences can be traced back to the different methods and basis sets used. The lifetime of the metastable N3 molecule is estimated to be ∼200 fs depending on the initial state of the reactants. Finally, neural-network-based exhaustive state-to-distribution models are presented using both PESs for the atom exchange reaction. These models will be instrumental for a broader exploration of the reaction dynamics of air.

Revealing new pathways for the reaction of Criegee intermediate CH2OO with SO2

Criegee intermediates play an important role in the tropospheric oxidation models through their reactions with atmospheric trace chemicals. We develop a global full-dimensional potential energy surface for the CH2OO + SO2 system and reveal how the reaction happens step by step by quasi-classical trajectory simulations. A new pathway forming the main products (CH2O + SO3) and a new product channel (CO2 + H2 + SO2) are predicted in our simulations. The new pathway appears at collision energies greater than 10 kcal/mol whose behavior demonstrates a typical barrier-controlled reaction. This threshold is also consistent with the ab initio transition state barrier height. For the minor products, a loose complex OCH2O ∙ ∙ ∙ SO2 is formed first, and then in most cases it soon turns into HCOOH + SO2, in a few cases it decomposes into CO2 + H2 + SO2 which is a new product channel, and rarely it remains as ∙OCH2O ∙ + SO2.

Multistate Dynamics and Kinetics of CO2 Activation by Ta+ in the Gas Phase: Insights into Single-Atom Catalysis.

The activation of carbon dioxide (CO2) by a transition-metal cation in the gas phase is a unique model system for understanding single-atom catalysis. The mechanism of such reactions is often attributed to a "two-state reactivity" model in which the high-energy barrier of a spin state correlating with ground-state reactants is avoided by intersystem crossing (ISC) to a different spin state with a lower barrier. However, such a "spin-forbidden" mechanism, along with the corresponding dynamics, has seldom been rigorously examined theoretically, due to the lack of global potential energy surfaces (PESs). In this work, we report full-dimensional PESs of the lowest-lying quintet, triplet, and singlet states of the TaCO2+ system, machine-learned from first-principles data. These PESs and the corresponding spin-orbit couplings enable us to provide an extensive theoretical characterization of the dynamics and kinetics of the reaction between the tantalum cation (Ta+) and CO2, which have recently been investigated experimentally at high collision energies using crossed beams and velocity map imaging, as well as at thermal energies using a selected-ion flow tube apparatus. The multistate quasi-classical trajectory simulations with surface hopping reproduce most of the measured product translational and angular distributions, shedding valuable light on the nonadiabatic reaction dynamics. The calculated rate coefficients from 200 to 600 K are also in good agreement with the latest experimental measurements. More importantly, these calculations revealed that the reaction is controlled by intersystem crossing, rather than potential barriers.

Molecular Dynamics Investigations of Dienolate [4 + 2] Reactions.

We report quantum mechanics calculations and quasiclassical trajectory simulations of [4 + 2] reactions using three common dienolate substrates: siloxy dienes, Li dienolates, and conjugated Pd enolates. Asynchronous transition structures and unequal bond formation were invariably found, with average time gaps of developing bonds ranging from 26.5 to >251.0 fs. The results display a spectrum of dynamically concerted and stepwise [4 + 2] reactions, offering insights into the origin of the stereochemical outcomes of such reactions.

Automated potential energy surface development and comprehensive dynamics for the F + CH3NH2 reaction.

This work is an extensive investigation of the F + CH3NH2 reaction dynamics using a newly-developed potential energy surface (PES). The full-dimensional spin-orbit (SO) corrected (MRCI+Q/aug-cc-pwCVDZ) PES is developed by the Robosurfer program package and the ManyHF method is used in order to fix the Hartree-Fock (HF) convergence issues in the entrance channel. On the surface, retrieved by the fitting of the iteratively extended set of the ManyHF-CCSD(T)-F12a/triple-zeta-quality and SO-corrected energy points, quasi-classical trajectory (QCT) simulations are run. By analyzing the opacity functions and integral cross sections (ICSs) of six reaction channels, the dynamics of the two most reactive hydrogen-abstraction reactions resulting in HF + CH2NH2/CH3NH products are selected for a thorough examination. Despite the statistically and thermodynamically expected results, the kinetically preferred amino hydrogen-abstraction is the dominant mechanism at low collision energies. The initial attack angle and scattering angle distributions are investigated as well. The post-reaction energy distributions show that the collision energy mostly converts into the translational energy of the products, while the reaction energy excites the vibration of the products. The computed vibrationally resolved rotational distributions and vibrational state distributions of the HF product are compared to experimental data, and the theory and experiment are found to be in good agreement.

Vibrational mode-specificity in the dynamics of the OH- + CH3I multi-channel reaction.

We report a comprehensive characterization of the vibrational mode-specific dynamics of the OH- + CH3I reaction. Quasi-classical trajectory simulations are performed at four different collision energies on our previously-developed full-dimensional high-level abinitio potential energy surface in order to examine the impact of four different normal-mode excitations in the reactants. Considering the 11 possible pathways of OH- + CH3I, pronounced mode-specificity is observed in reactivity: In general, the excitations of the OH- stretching and CH stretching exert the greatest influence on the channels. For the SN2 and proton-abstraction products, the reactant initial attack angle and the product scattering angle distributions do not show major mode-specific features, except for SN2 at higher collision energies, where forward scattering is promoted by the CI stretching and CH stretching excitations. The post-reaction energy flow is also examined for SN2 and proton abstraction, and it is unveiled that the excess vibrational excitation energies rather transfer into the product vibrational energy because the translational and rotational energy distributions of the products do not represent significant mode-specificity. Moreover, in the course of proton abstraction, the surplus vibrational energy in the OH- reactant mostly remains in the H2O product owing to the prevailing dominance of the direct stripping mechanism.

High-level analytical potential-energy-surface-based dynamics of the OH- + CH3CH2Cl SN2 and E2 reactions in full (24) dimensions.

We develop a coupled-cluster full-dimensional global potential energy surface (PES) for the OH- + CH3CH2Cl reactive system, using the Robosurfer program package, which automatically samples configurations along PES-based trajectories as well as performs ab initio computations with Molpro and fitting with the monomial symmetrization approach. The analytical PES accurately describes both the bimolecular nucleophilic substitution (SN2) and elimination (E2) channels leading to the Cl- + CH3CH2OH and Cl- + H2O + C2H4 products, respectively, and allows efficient quasi-classical trajectory (QCT) simulations. QCT computations on the new PES provide accurate statistically-converged integral and differential cross sections for the OH- + CH3CH2Cl reaction, revealing the competing dynamics and mechanisms of the SN2 and E2 (anti, syn, β-α transfer) channels as well as various additional pathways leading to induced inversion of the CH3CH2Cl reactant, H-exchange between the reactants, H2O⋯Cl- complex formation, and H2O + CH3CHCl- products via proton abstraction.

ManyHF-based full-dimensional potential energy surface development and quasi-classical dynamics for the Cl + CH3NH2 reaction.

A full-dimensional spin-orbit (SO)-corrected potential energy surface (PES) is developed for the Cl + CH3NH2 multi-channel system. Using the new PES, a comprehensive reaction dynamics investigation is performed for the most reactive hydrogen-abstraction reactions forming HCl + CH2NH2/CH3NH. Hartree-Fock (HF) convergence problems in the reactant region are handled by the ManyHF method, which finds the lowest-energy HF solution considering several different initial guess orbitals. The PES development is carried out with the Robosurfer program package, which iteratively improves the surface. Energy points are computed at the ManyHF-UCCSD(T)-F12a/cc-pVDZ-F12 level of theory combined with basis set (ManyHF-RMP2-F12/cc-pVTZ-F12 - ManyHF-RMP2-F12/cc-pVDZ-F12) and SO (MRCI+Q/aug-cc-pwCVDZ) corrections. Quasi-classical trajectory simulations show that the CH3-side hydrogen abstraction occurs more frequently in contrast to the NH2-side reaction. In both cases, the integral cross sections decrease with increasing collision energy (Ecoll). A reaction mechanism shifting from indirect to direct stripping can be observed from the opacity functions, scattering angle, and translation energy distributions as Ecoll increases. Initial attack angle distributions reveal that chlorine prefers to abstract hydrogen from the approached functional group. The collision-energy dependence of the product energy distributions shows that the initial translational energy mainly transfers to product recoil. The HCl vibrational and rotational energy values are comparable and nearly independent of collision energy, while the CH2NH2 and CH3NH co-products' vibrational energy values are higher than the rotational energy values with more significant Ecoll dependence. The HCl(v = 0) rotational distributions are compared with experiment, setting the direction for future investigations.

Toward a Unified Analytical Description of Internal Conversion and Intersystem Crossing in the Photodissociation of Thioformaldehyde. I. Diabatic Singlet States.

The photodissociation of thioformaldehyde is an archetypal system for the study of competition between internal conversion and intersystem crossing, which involves its two singlet states (S0 and S1) and two triplet states (T1 and T2). In order to perform accurate dynamic simulations, either quantum or quasi-classical, it is essential to construct an analytical representation for all necessary electronic structure data. In this work, a diabatic potential energy matrix (DPEM), Hd, for the two singlet states (S0 and S1) is reported. The analytical form of DPEM is symmetrized and constructed to reproduce adiabatic energies, energy gradients, and derivative couplings obtained from high-level multireference configuration interaction wave functions. The Hd is fully saturated in the molecular configuration space with a trajectory-guided point sampling approach. This Hd can provide the accurate description of the photodissociation of thioformaldehyde on its singlet states and is also a necessary part for incorporating the spin-orbit couplings into a unified diabatic framework. Preliminary quasi-classical trajectory simulations show that a roaming mechanism also exists in the molecular dissociation channel of thioformaldehyde.

Molecular dynamics simulations and machine-learning assisted study of the reaction path bifurcation: Application to the intramolecular Diels–Alder cycloaddition between cyclobutadiene and butadiene

The intramolecular Diels–Alder cycloaddition between cyclobutadiene and butadiene, which involves post-transition-state bifurcation (PTSB), has been investigated using the ring-polymer molecular dynamics (RPMD), classical MD and quasi-classical trajectory (QCT) simulations, and supervised machine-learning (ML) technique. The branching fraction of this reaction strongly depends on the simulation temperature. While QCT, classical MD and RPMD simulations performed at room temperature, starting from the ambimodal transition state (TS), showed the similar dynamics, QCT overestimated the minor branching fraction at low temperature. The supervised machine-learning analysis revealed that the initial coordinates and momenta for low frequency modes at the ambimodal TS contribute to the branching dynamics. The classical MD and RPMD methods follow similar conditions to quantum Boltzmann distributions, whereas the artificially localized phase distribution, considering that the zero-point energy is wedged into the classical particles. As a result, the QCT method can provide inadequate bifurcation dynamics, such as the overestimation of the minor product.

Inelastic scattering of OH from a liquid PFPE surface: Resolution of correlated speed and angular distributions.

Inelastic collisions of OH with an inert liquid perfluoropolyether (PFPE) surface have been studied experimentally. A pulsed molecular beam of OH with a kinetic energy distribution peaking at 35 kJ mol-1 was directed at a continually refreshed PFPE surface. OH molecules were detected state-selectively with spatial and temporal resolution by pulsed, planar laser-induced fluorescence. The scattered speed distributions were confirmed to be strongly superthermal, regardless of the incidence angle (0° or 45°). Angular scattering distributions were measured for the first time; their reliability was confirmed through extensive Monte Carlo simulations of experimental averaging effects, described in Paper II [A. G. Knight et al., J. Chem. Phys. 158, 244705 (2023)]. The distributions depend markedly on the incidence angle and are correlated with scattered OH speed, consistent with predominantly impulsive scattering. For 45° incidence, the angular distributions are distinctly asymmetric to the specular side but peak at sub-specular angles. This, along with the breadth of the distributions, is incompatible with scattering from a surface that is flat on a molecular scale. New molecular dynamics simulations corroborate the roughness of the PFPE surface. A subtle but unexpected systematic dependence of the angular distribution on the OH rotational state was found, which may be dynamical in origin. The OH angular distributions are similar to those for kinematically similar Ne scattering from PFPE and hence not strongly perturbed by OH being a linear rotor. The results here are broadly compatible with prior predictions from independent quasiclassical trajectory simulations of OH scattering from a model-fluorinated self-assembled monolayer surface.

Exploring the versatile reactivity of the F- + SiH3Cl system on a full-dimensional coupled-cluster potential energy surface.

We develop a full-dimensional analytical potential energy surface (PES) for the F- + SiH3Cl reaction using Robosurfer for automatically sampling the configuration space, the robust [CCSD-F12b + BCCD(T) - BCCD]/aug-cc-pVTZ composite level of theory for computing the energy points, and the permutationally invariant polynomial method for fitting. Evolution of the fitting error and the percentage of the unphysical trajectories are monitored as a function of the iteration steps/number of energy points and polynomial order. Quasi-classical trajectory simulations on the new PES reveal rich dynamics resulting in high-probability SN2 (SiH3F + Cl-) and proton-transfer (SiH2Cl- + HF) products as well as several lower-probability channels, such as SiH2F- + HCl, SiH2FCl + H-, SiH2 + FHCl-, SiHFCl- + H2, SiHF + H2 + Cl-, and SiH2 + HF + Cl-. The Walden-inversion and front-side-attack-retention SN2 pathways are found to be competitive, producing nearly racemic products at high collision energies. The detailed atomic-level mechanisms of the various reaction pathways and channels as well as the accuracy of the analytical PES are analyzed along representative trajectories.

Dynamics of the Cl- + CH3I reaction on a high-level abinitio analytical potential energy surface.

We have developed a full-dimensional analytical abinitio potential energy surface (PES) for the Cl- + CH3I reaction using the Robosurfer program system. The energy points have been computed using a robust composite method defined as CCSD-F12b + BCCD(T) - BCCD with the aug-cc-pVTZ(-PP) basis set and have been fitted by the permutationally invariant polynomial approach. Quasi-classical trajectory simulations on the new PES reveal that two product channels are open in the collision energy (Ecoll) range of 1-80 kcal/mol, i.e., SN2 leading to I- + CH3Cl and iodine abstraction (above ∼45 kcal/mol) resulting in ICl- + CH3. Scattering angle, initial attack angle, product translational energy, and product internal energy distributions show that the SN2 reaction is indirect at low Ecoll and becomes direct-rebound-back-side (CH3-side) attack-type, as Ecoll increases. Iodine abstraction mainly proceeds with direct stripping mechanism with side-on/back-side attack preference. Comparison with crossed-beam experiments and previous direct dynamics simulations shows quantitative or qualitative agreement and also highlights possible theoretical and/or experimental issues motivating further research.

CO Inversion on a NaCl(100) Surface: A Multireference Quantum Embedding Study.

We develop a multireference quantum embedding model to investigate a recent experimental observation of the isomerization of vibrationally excited CO molecules on a NaCl(100) surface [Science 2020, 367, 175-178]. To explore this mechanism, we built a reduced potential energy surface of CO interacting with NaCl(100) using a second-order multireference perturbation theory, modeling the adsorbate-surface interaction with our previously developed active space embedding theory (ASET). We considered an isolated CO molecule on NaCl(100) and a high-coverage CO monolayer (1/1), and for both we generated potential energy surfaces parametrized by the CO stretching, adsorption, and inversion coordinates. These surfaces are used to determine stationary points and adsorption energies and to perform a vibrational analysis of the states relevant to the inversion mechanism. We found that for near-equilibrium bond lengths, CO adsorbed in the C-down configuration is lower in energy than in the O-down configuration. Stretching of the C-O bond reverses the energetic order of these configurations, supporting the accepted isomerization mechanism. The vibrational constants obtained from these potential energy surfaces show a small (< 10 cm-1) blue- and red-shift for the C-down and O-down configurations, respectively, in agreement with experimental assignments and previous theoretical studies. Our vibrational analysis of the monolayer case suggests that the O-down configuration is energetically more stable than the C-down one beyond the 16th vibrational excited state of CO, a value slightly smaller than the one from quasi-classical trajectory simulations (22nd) and consistent with the experiment. Our analysis suggests that CO-CO interactions in the monolayer play an important role in stabilizing highly vibrationally excited states in the O-down configuration and reducing the barrier between the C-down and O-down geometries, therefore playing a crucial role in the inversion mechanism.

Post-dissociation Dynamics of N2 on Ru(0001): How Far Can the “Hot” N Atoms Travel?

Due to the high barrier and large exoergicity, the dissociation of N2 impinging on Ru(0001) produces ballistic N atoms that can travel significant distances from the impact site, as shown by a recent scanning tunneling microscopy study [Wagner, J. J. Phys. Chem. C 2022, 126, 18333−18342]. In this work, the “hot” nitrogen atom dynamics following N2 dissociation is investigated theoretically on a high-dimensional potential energy surface based on a neural network representation of density functional theory data. Quasi-classical trajectory simulations for N2 dissociation with several initial conditions revealed that typically only one N atom undergoes significant migration, while the other is often trapped near the impact site. Regardless of the initial condition, the average final separation between the two N atoms is typically less than 10 Å, about 1 order of magnitude less than the experimental report (66 ± 28 Å). The relatively short migration distance of the hot N atom found in our simulations is attributed to a high diffusion barrier and fast energy dissipation to surface phonons. The theory–experiment discrepancy presents a challenge to the quantitative understanding of hot atom dynamics on metal surfaces.

Quasiclassical Trajectory Simulation as a Protocol to Build Locally Accurate Machine Learning Potentials.

Direct trajectory calculations have become increasingly popular in recent computational chemistry investigations. However, the exorbitant computational cost of ab initio trajectory calculations usually limits its application in mechanistic explorations. Recently, machine learning-based potential energy surface (ML-PES) provides a powerful strategy to circumvent the heavy computational cost and meanwhile maintain the required accuracy. Despite the appealing potential, constructing a robust ML-PES is still challenging since the training set of the PES should cover a broad enough configuration space. In this work, we demonstrate that when the concerned properties could be collected by the localized sampling of the configuration space, quasiclassical trajectory (QCT) calculations can be invoked to efficiently obtain locally accurate ML-PESs. We prove our concept with two model reactions: methyl migration of i-pentane cation and dimerization of cyclopentadiene. We found that the locally accurate ML-PESs are sufficiently robust for reproducing the static and dynamic features of the reactions, including the time-resolved free energy and entropy changes, and time gaps.

Competition between the H-abstraction and the X-abstraction pathways in the HX (X = Br, I) + C2H5 reactions.

The recently-developed high-level full-dimensional spin-orbit-corrected potential energy surfaces based on ManyHF-UCCSD(T)-F12a/cc-pVDZ-F12 + SOcorr(MRCI-F12+Q(5,3)/cc-pVDZ-F12) (cc-pVDZ-PP-F12 for the Br and I atoms) energy points for the reactions of HX (X = Br, I) with C2H5 are improved by adding three to four thousand new geometries with higher energies at the same ab initio level to cover a higher-energy range. Quasi-classical trajectory simulations in the 30-80 kcal mol-1 collision energy range on the new surfaces are performed and show that as collision energy increases, the reaction probability of the submerged-barrier H-abstraction reaction pathway decreases a bit but the reactivity of the X-abstraction reaction, which has an apparent barrier, increases significantly, which leads to the co-domination of the two reaction pathways at high collision energies. The excitation in HX vibrational mode helps both reaction pathways, but more for X-abstraction. The mode-specific excitations in C2H5 inhibit the H-abstraction, especially for CH2 wagging mode, but almost no effect is found for X-abstraction. The deuterium effect is similar for both pathways. The sudden vector projection model can only predict the HX-stretching vibrational enhancements in X-abstraction. Forward/backward scattering is favored for H/X-abstraction, indicating the dominance of the direct stripping/rebound mechanism. The decrease of reactivity for the H-abstraction reaction pathway partly comes from the fact that the H-abstraction is much pickier about the initial attack angle. The reactivity of both reaction pathways increases when side-on CH3CH2 attack happens. The major part of the initial translational energy is preserved as translational energy in the products in H-abstraction, while for X-abstraction a large amount of it is transferred into the internal energy of C2H5X.